A softener when programmed properly, will soften to 0 grains hardness. Even at that, it may not be completely soft. As one 'grain' is equivalent to 17 ppm of hardness, a test indicating 'O' grains may be somewhere between 0 ppm and 16 ppm hardness. If in the upper range, it may not feel as slippery soft as water in the lower range. A Hach 5b is the most recommended softness test kit for testing 'grains' as 'feel' is not a measurable indicator.
Perhaps your neutralizer hadn't been working properly before being serviced. You may wish to obtain a pH tester to be able to periodically monitor the neutralizer effectiveness (ie: pre-neutralizer vs post neutralizer).
I'm not certain if it's possible to overdo neutralizing thereby raising the water pH much higher than 7.0? I do know that high pH liquids will feel very slippery to touch (ie: liquid dishwasher detergent or chlorine bleach).